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Leader-Following Consensus of Fractional-Order Uncertain Multi-Agent Systems with Time Delays

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Abstract

This paper investigates the leader-following consensus of fractional-order uncertain multi-agent systems (FOUMASs) with time delays. Based on algebraic graph theory, Lyapunov stability theory, Laplace transform and linear matrix inequalities (LMIs), some sufficient conditions are achieved to realize leader-following consensus of FOUMASs. In addition, such results can be extended to the case of directed topologies and FOUMASs without time delays. Through numerical simulations, the authenticity and validity of results are verified.

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References

  1. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49:1520–1533

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen X, Hao F (2014) Event-triggered consensus control of second-order multi-agent systems. Asian J Control 17:592–603

    Article  MathSciNet  MATH  Google Scholar 

  3. Syed Ali M, Agalya R, Orman Z, Arik S (2020) Leader-following consensus of non-linear multi-agent systems with interval time-varying delay via impulsive control. Neural Process Lett 53:69–83

    Google Scholar 

  4. Liu XY, Fu HB, Lei L (2020) Leader-following mean square consensus of stochastic multi-agent systems via periodically intermittent event-triggered control. Neural Process Lett 53:275–298

    Article  Google Scholar 

  5. Fax JA, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49:1465–1476

    Article  MathSciNet  MATH  Google Scholar 

  6. Dong RS, Geng ZY (2015) Consensus for formation control of multi-agent systems. Int J Robust Nonlinear Control 25:2481–2501

    Article  MathSciNet  MATH  Google Scholar 

  7. Lin P, Jia YM (2010) Distributed rotating formation control of multi-agent systems. Syst Control Lett 59:587–595

    Article  MathSciNet  MATH  Google Scholar 

  8. Meng DY, Jia YM (2014) Formation control for multi-agent systems through an iterative learning design approach. Int J Robust Nonlinear Control 24:340–361

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu S, Xie LH, Zhang HS (2014) Containment control of multi-agent systems by exploiting the control inputs of neighbors. Int J Robust Nonlinear Control 24:2803–2818

    Article  MathSciNet  MATH  Google Scholar 

  10. Song Q, Liu F, Su HS, Vasilakos AV (2016) Semi-global and global containment control of multi-agent systems with second-order dynamics and input saturation. Int J Robust Nonlinear Control 26:3460–3480

    Article  MathSciNet  MATH  Google Scholar 

  11. Hu JQ, Yu J, Cao JD (2016) Distributed containment control for nonlinear multi-agent systems with time-delayed protocol. Asian J Control 18:747–756

    Article  MathSciNet  MATH  Google Scholar 

  12. Li ZK, Ren W, Liu XD, Fu MY (2013) Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int J Robust Nonlinear Control 23:534–547

    Article  MathSciNet  MATH  Google Scholar 

  13. Xie DM, Liu QL, Lv LF, Li SY (2014) Necessary and sufficient condition for the group consensus of multi-agent systems. Appl Math Comput 243:870–878

    MathSciNet  MATH  Google Scholar 

  14. Ge XH, Han QL, Ding DR, Zhang XM, Ning BD (2018) A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems. Neurocomputing 275:1684–1701

    Article  Google Scholar 

  15. Dong XW, Hu GQ (2017) Time-varying formation tracking for linear multiagent systems with multiple leaders. IEEE Trans Autom Control 62:3658–3664

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen YL, Hu TT, Li YH, Zhong SM (2021) Consensus of fractional-order multi-agent systems with uncertain topological structure: a Takagi-Sugeno fuzzy event-triggered control strategy. Fuzzy Set Syst 416:64–85

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu B, Su HS, Wu LC, Li XL, Lu X (2021) Fractional-order controllability of multi-agent systems with time-delay. Neurocomputing 424:268–277

    Article  Google Scholar 

  18. Wang JJ, Zhou JQ, Mo YJ, Li LX (2020) Consensus tracking via iterative learning control for singular fractional-order multi-agent systems under iteration-varying topologies and initial state errors. IEEE Access 8:168812–168824

    Article  Google Scholar 

  19. Shahamatkhah E, Tabatabaei M (2020) Containment control of linear discrete-time fractional-order multi-agent systems with time-delays. Neurocomputing 385:42–47

    Article  Google Scholar 

  20. Gao ZY, Zhang HG, Wang YC, Zhang K (2020) Leader-following consensus conditions for fractional-order descriptor uncertain multi-agent systems with \(0<\alpha <2\) via output feedback control. J Frankl Inst 357:2263–2281

    Article  MathSciNet  MATH  Google Scholar 

  21. Song C, Cao JD, Liu YZ (2015) Robust consensus of fractional-order multi-agent systems with positive real uncertainty via second-order neighbors information. Neurocomputing 165:293–299

    Article  Google Scholar 

  22. Yin XX, Hu SL (2013) Consensus of fractional-order uncertain multi-agent systems based on output feedback. Asian J Control 15:1538–1542

    MathSciNet  MATH  Google Scholar 

  23. Zhu W, Chen B, Jie Y (2017) Consensus of fractional-order multi-agent systems with input time delay. Fract Calc Appl Anal 20:52

    Article  MathSciNet  MATH  Google Scholar 

  24. Yang HY, Zhu LX, Cao KC (2014) Distributed coordination of fractional order multi-agent systems with communication delays. Fract Calc Appl Anal 17:23–37

    Article  MathSciNet  MATH  Google Scholar 

  25. Lv SS, Pan M, Li XG, Cai WY, Lan TY, Li BQ (2019) Consensus control of fractional-order multi-agent systems with time delays via fractional-order iterative learning control. IEEE Access 7:159731–159742

    Article  Google Scholar 

  26. Hu W, Wen GG, Rahmani A, Bai J, Yu YG (2020) Leader-following consensus of heterogenous fractional-order multi-agent systems under input delays. Asian J Control 22:2217–2228

    Article  MathSciNet  Google Scholar 

  27. Chen C, Ding ZX, Li S, Wang LH (2020) Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions. Chin Phys B 29:040202

    Article  Google Scholar 

  28. Wang XH, Li XS, Huang NJ, Regan D (2019) Asymptotical consensus of fractional-order multi-agent systems with current and delay states. Appl Math Mech 40:1677–1694

    Article  MathSciNet  MATH  Google Scholar 

  29. Bai J, Wen GG, Rahmani A (2017) Distributed consensus tracking for the fractional-order multi-agent systems based on the sliding mode control method. Neurocomputing 235:210–216

    Article  Google Scholar 

  30. Wang H, Yu YG, Wen GG, Zhang S, Yu JZ (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23

    Article  Google Scholar 

  31. Li Y, Chen YQ, Wang YC, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput Math Appl 59:1810–1821

    Article  MathSciNet  MATH  Google Scholar 

  32. Zheng GM, Zhong XL, Zeng QC (2016) Leader-following consensus of multi-agent system with a smart leader. Neurocomputing 214:401–408

    Article  Google Scholar 

  33. Wang FY, Zhong XL, Zeng QC (2018) A novel leader-following consensus of multi-agent systems with smart leader. Int J Control Autom Syst 16:1483–1492

    Article  Google Scholar 

  34. Zhu W, Jiang ZP (2015) Event-based leader-following consensus of multi-agent systems with input time delay. IEEE Trans Autom Control 60:1362–1367

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) under Grant Y202002.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    Hailang Yang, Sai Li, Le Yang & Zhixia Ding

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  1. Hailang Yang
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  2. Sai Li
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  3. Le Yang
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  4. Zhixia Ding
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Correspondence to Zhixia Ding.

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Project supported by the Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology) (Grant No. Y202002).

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Yang, H., Li, S., Yang, L. et al. Leader-Following Consensus of Fractional-Order Uncertain Multi-Agent Systems with Time Delays. Neural Process Lett 54, 4829–4849 (2022). https://doi.org/10.1007/s11063-022-10837-2

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  • DOI: https://doi.org/10.1007/s11063-022-10837-2

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